Eigen Decompositions of Covariance Matrices on a Fixed Point DSP

A number of signal processing algorithms can profitably use the eigenvalue decomposition (EVD) of a covariance matrix. Since many of these algorithms are implemented on fixed-point Digital Signal Processors, there is interest in symmetric EVD algorithms that can be implemented in fixed-point arithmetic. Modifications to Jacobi Cyclic algorithms are proposed which make them amenable to fixed-point implementation. We present the algorithms in detail and propose criteria to be used in evaluating the quality of an algorithm's output. The fixed–point algorithm was implemented on a TMS320C6211 fixed point DSP and we present results that show that the EVDs of covariance matrices obtained are comparable to those obtained using Jacobi algorithms performed in high-precision floating point arithmetic.

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